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Physics 234

Intermediate Methods of Mathematical Physics II
Professor Alexander Lisyansky, office hours: Wednesday, 12-1 pm
  1. In Physics 234 we will discuss some of the most important mathematical methods that physicists use to solve problems in their field.  These methods include:
    1. Complex analysis
    2. Fourier series and transforms
    3. Laplace transforms.
The course is definitely math intensive.  However, it is radically different from a typical math course. Rather than emphasizing the theoretical underpinnings of various theorems and techniques, we will focus on their use in problem solving.  The purpose of the course is to substantially increase your mathematical and problem solving skills.
  1. Physics 233 and 234 are independent courses.
  2. Math requirements: I do not expect you to know any math beyond differentiation and integration, but you must know those topics well.  Before taking either of these courses, you should go over the chain rule for differentiation, integration by substitution, and by parts.  
  3. Physics requirements: I assume that everybody passed Physics 145 and 146 and retained what they learned.
Textbook
                Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition (Wiley, 2011)
Assessment
  1. There will be three exams: two midterms and a final. The first and second midterms and the final comprise 15%, 25%, and 45% of the course grade, respectively.
  2. Homework makes 15% of the course grade.
Homework
  1. The following point cannot be emphasized strongly enough: to use mathematics effectively, you need not just knowledge but skills as well. The only way to develop your math skills is by solving many problems. Therefore, the homework assignments are the essential part of the course.
    1. The majority of problems in your homework assignments are easy.  So, as long as you’ve read the related chapter, it should take a couple of minutes to solve many of them.  The other ones are harder and require more time.  In any case, if you solve all the assigned problems, I am certain that you will not only pass the course, but will earn a respectable grade.  If you chose not to do the homework assignments, I can almost guarantee that you are setting yourself to fail the course.
    2. It is extremely important to understand that watching someone solve a problem when you have not yet attempted it yourself is of little or no benefit. Students must at least attempt to solve homework problems before seeing the correct solution if they expect to make any progress in the course. Your aim is to solve problems on your own without looking at the solution.  To get to this level requires a great deal of time and commitment.  If you know that you are not going to be able to make this kind of commitment, it’s better to drop the course now.
  2. To make your life easier, we will have problem solving sessions about every two weeks (usually on Mondays).  You will tell me which problems you had difficulty solving at home, and I will either solve them for you or at least give directions as to how to solve them.
  3. There is no way that I will have enough time to solve the majority or even half of the homework problems in class, therefore I will be solving only the problems that you struggled with at home.
  4. When you see the solution of a problem in class and copy it into your notebook, it may give you the false impression that now you know how to solve the problem and can repeat the solution anytime. I want to reiterate that only when you can handle a problem without looking at your notes, you will then be truly prepared to solve it during an exam.
  5. The problems that correspond to a particular section must be solved within a week after the section is covered during the lecture.  To assure that you solve problems on time, I will not entertain any questions related to problems from sections covered during the previous problem solving session.
  6. No late homework will be accepted.
  7. Homework will be graded on a scale from 0 to 2.
  8. I will not be able to discuss homework grades.
  9. The homework for the preceding week will be collected on Mondays.
Exams
  1. To make your life even easier, all exams will be open book exams so that you do not need to memorize formulas (except, of course, basic formulas such as trigonometric identities, basic integrals, etc., that by now you must know anyway).
    1. You will not be able to use your own textbooks during the exam. Instead, you will be given printouts of the corresponding chapters of the textbook.
    2. I want to warn you about another false impression.  Since you are allowed to use your textbook during the exam, you may convince yourself that this will be enough to help you solve problems you have not mastered on your own.  Take my word for it - it’s not!  Perhaps, if there were one or two questions on an exam, you could rely on the text in this manner.  However, you will have many more problems (in the neighborhood of 15 and 20 problems on midterms and final exams, respectively).  That translates into an average of 5-7 minutes per problem.  If you need to spend time flipping through pages, reviewing the proper approach to various problems, you will most certainly fail the exam. You can get a decent grade (read ‘A’) if and only if you know the material very well, and you have highly developed mathematical skills. This is what I am hoping you will acquire in this course.
  2. To add an incentive to do homework, I will choose all problems for both midterm and final exams from the homework set.
  3. Graphing calculators cannot be used during the exams
Policies
  1. Feel free to interrupt me any time with any questions related to the topic under discussion
  2. At about 9:30 am (in 15 min of the class start) I will close the door and will not let anyone in. Please do not be late.
 
Lastly, I want to wish you all the best and remember there is no substitute for diligence and perseverance.

Homework problems for
Physics 234, Intermediate Methods of Mathematical Physics II
 
Textbook: Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition (Wiley, 2011)
 
Chapter 13
Sec. 13.1: 1–5, 8–20
Sec. 13.2: 1–7, 9–15, 17, 18, 21, 22, 24–27
Sec. 13.3: 2–8, 11, 14–16, 20, 21
Sec. 13.4: 1–4, 8, 11, 12–14, 18, 22
Sec. 13.5: 2–6, 8–10, 13–16, 19, 21, 22
Sec. 13.6: 4, 6–8, 10–13, 17–19
Sec. 13.7: 5–8, 11–16, 18–20, 22–24, 26, 27
 
Chapter 14
Sec. 14.1: 1–4, 9–14, 16, 19–24, 30
Sec. 14.2: 2, 4, 9, 11, 15, 21, 22, 24, 25, 27
Sec. 14.3: 1–8, 12, 13, 15–17
Sec. 14.4: 1–3, 5, 6, 9–14
 
Chapter 15
Sec. 15.4: 3–6, 9, 18, 19
 
Chapter 16
Sec. 16.1: 1–6, 9, 10, 14, 15, 19–21
Sec. 16.2: 1–3, 5, 9, 13–15, 18
Sec. 16.3: 3–7, 9, 11, 12, 14, 16, 22, 24
Sec. 16.4: 1, 2, 4–6, 11, 13, 14, 16, 17, 20–23, 25, 26
 
Chapter 11
Sec. 11.1: 1–3, 5–9, 12–14, 17
Sec. 11.2: 1–11, 13, 14, 17, 18
Sec. 11.7: 1–4, 7, 8, 11, 12, 16–19
Sec. 11.8: 1, 3, 5, 9–11
Sec. 11.9: 2–7, 9–11
 
Chapter 6
Sec. 6.1:    1, 3, 5–7, 9–14, 16, 23, 25–27, 29–32, 33–35, 37, 38, 40–42, 44, 45
Sec. 6.2:    1–10, 12, 13, 16–19,  23–25, 27
Sec. 6.3:    2–8, 12–15, 18, 19, 21, 22, 25, 29, 31, 32, 35, 38
Sec. 6.4:    3–5, 6, 8–11
Sec. 6.5:    1–6, 8–10, 17–22
Sec. 6.6:    2–4, 8, 11, 14, 15, 17, 20